As a result of the global pandemic caused by COVID-19, universities have carried out teaching in a digital way, accelerating the inclusion and use of technologies in methodological adaptation. The research aims to ascertain the perception that students at the Faculty of Education Sciences of the University of Granada have regarding the pedagogical model adopted in the virtual learning environment during confinement through the second semester of the 2019–2020 academic year. The information collection method was an online questionnaire, using simple random sampling with proportional affixing 0.5, 95% confidence level and maximum permissible error of 4.7%. The results demonstrate a generalised dissatisfaction of the students, being fundamental to carry out the transition of the educational processes and training of the teaching staff. The implementation of active methodologies increases due to the virtual condition, specifically the flipped classroom methodology, but students manifest generalised dissatisfaction regarding the adequate methodological development and the involvement of professors. There is an outstanding use of e-mail and the virtual learning platform (PRADO), although they consider that they do not have the appropriate knowledge about image editors, video, computer graphics, synchronous response systems and anti-plagiarism tools. The students surveyed express that the tutoring functions, tasks and beliefs of the teaching staff in e-learning are not satisfactory.

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Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.

Faced with novel coronavirus outbreak, the most hard-hit countries adopted a lockdown strategy to contrast the spread of virus. Many studies have already documented that the COVID-19 control actions have resulted in improved air quality locally and around the world. Following these lines of research, we focus on air quality changes in the urban territory of Chieti-Pescara (Central Italy), identified as an area of criticality in terms of air pollution. Concentrations of $$\hbox {NO}_{{2}}$$ NO 2 , $$\hbox {PM}_{{10}}$$ PM 10 , $$\hbox {PM}_{2.5}$$ PM 2.5 and benzene are used to evaluate air pollution changes in this Region. Data were measured by several monitoring stations over two specific periods: from 1st February to 10 th March 2020 (before lockdown period) and from 11st March 2020 to 18 th April 2020 (during lockdown period). The impact of lockdown on air quality is assessed through functional data analysis. Our work makes an important contribution to the analysis of variance for functional data (FANOVA). Specifically, a novel approach based on multivariate functional principal component analysis is introduced to tackle the multivariate FANOVA problem for independent measures, which is reduced to test multivariate homogeneity on the vectors of the most explicative principal components scores. Results of the present study suggest that the level of each pollutant changed during the confinement. Additionally, the differences in the mean functions of all pollutants according to the location and type of monitoring stations (background vs traffic), are ascribable to the $$\hbox {PM}_{{10}}$$ PM 10 and benzene concentrations for pre-lockdown and during-lockdown tenure, respectively. FANOVA has proven to be beneficial to monitoring the evolution of air quality in both periods of time. This can help environmental protection agencies in drawing a more holistic picture of air quality status in the area of interest.

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A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.

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